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Of the following quantities, which one has dimension different from the remaining three? [1989]
- a)Energy per unit volume
- b)Force per unit area
- c)Product of voltage and charge per unit volume
- d)Angular momentum.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Of the following quantities, which one has dimension different from th...
For angular momentum, the dimensional formula is ML2T–1. For other three, it is ML2T–2.
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Of the following quantities, which one has dimension different from th...
Dimensional analysis is a tool used to check the correctness of an equation or to derive a formula for a physical quantity. It involves analyzing the dimensions of the physical quantities involved in the equation. The dimensions of a physical quantity are the powers to which the fundamental units of length, mass, and time are raised in the expression for the quantity.
In this question, we are given four physical quantities and we have to determine which one has a different dimension from the other three. Let us analyze each quantity in turn:
a) Energy per unit volume: The dimension of energy is [M L^2 T^-2] and the dimension of volume is [L^3]. Therefore, the dimension of energy per unit volume is [M L^-1 T^-2].
b) Force per unit area: The dimension of force is [M L T^-2] and the dimension of area is [L^2]. Therefore, the dimension of force per unit area is [M L^-1 T^-2].
c) Product of voltage and charge per unit volume: The dimension of voltage is [M L^2 T^-3 I^-1] and the dimension of charge is [T I]. Therefore, the dimension of voltage and charge per unit volume is [M L^-1 T^-1 I^-1].
d) Angular momentum: The dimension of angular momentum is [M L^2 T^-1].
Comparing the dimensions of the four quantities, we can see that option D (angular momentum) has a different dimension from the other three. Therefore, the correct answer is option D.
In summary:
- Energy per unit volume: [M L^-1 T^-2]
- Force per unit area: [M L^-1 T^-2]
- Product of voltage and charge per unit volume: [M L^-1 T^-1 I^-1]
- Angular momentum: [M L^2 T^-1]
Note that we did not use any specific formula or equation for this analysis, only the fundamental dimensions of the quantities involved.
In this question, we are given four physical quantities and we have to determine which one has a different dimension from the other three. Let us analyze each quantity in turn:
a) Energy per unit volume: The dimension of energy is [M L^2 T^-2] and the dimension of volume is [L^3]. Therefore, the dimension of energy per unit volume is [M L^-1 T^-2].
b) Force per unit area: The dimension of force is [M L T^-2] and the dimension of area is [L^2]. Therefore, the dimension of force per unit area is [M L^-1 T^-2].
c) Product of voltage and charge per unit volume: The dimension of voltage is [M L^2 T^-3 I^-1] and the dimension of charge is [T I]. Therefore, the dimension of voltage and charge per unit volume is [M L^-1 T^-1 I^-1].
d) Angular momentum: The dimension of angular momentum is [M L^2 T^-1].
Comparing the dimensions of the four quantities, we can see that option D (angular momentum) has a different dimension from the other three. Therefore, the correct answer is option D.
In summary:
- Energy per unit volume: [M L^-1 T^-2]
- Force per unit area: [M L^-1 T^-2]
- Product of voltage and charge per unit volume: [M L^-1 T^-1 I^-1]
- Angular momentum: [M L^2 T^-1]
Note that we did not use any specific formula or equation for this analysis, only the fundamental dimensions of the quantities involved.
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